PARAMETER INFERENCE FOR TIME-SERIES WITH REGULAR AND SEASONAL UNIT ROOTS

It is common to have both regular and seasonal roots present in many time series data. It may occur that one or both of the roots are just close but not equal to unity. Parameter inference for this situation is considered both when the time series has a finite or an infinite variance. Asymptotic characterizations of the test statistics were obtained via functionals of Ornstein-Uhlenbeck processes and Levy processes. Tabulations for the large sample distributions are obtained. The results will be useful in applications deciding whether both regular and seasonal differencing are needed in fitting a time series model.